Theorems · Theorem · combinatorics
Fintype.card_le_of_surjective
∀ {α : Type u_1} {β : Type u_2} [inst : Fintype α] [inst_1 : Fintype β] (f : α → β),
Function.Surjective f → Fintype.card β ≤ Fintype.card α- Defined in
- Mathlib.Data.Fintype.Card
- Cited by
- 10 results in Mathlib
- Foundations
- Depth 81 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Fintypestatement and proof · cited by 7,736
- Fintype.cardstatement · cited by 1,386
- Function.surjInvproof · cited by 63
- Fintype.card_le_of_injectiveproof · cited by 19
- Function.injective_surjInvproof · cited by 14
Cited by10
Results whose statement or proof uses this declaration.
- SimplexCategory.len_le_of_epiproof · cited by 9
- Fintype.card_range_leproof · cited by 4
- Matrix.Nonsingular.of_linearIndependent_colproof · cited by 3
- Configuration.HasLines.card_leproof · cited by 2
- SimpleGraph.card_le_chromaticNumber_iff_forall_surjectiveproof · cited by 2
- Function.LeftInverse.rightInverse_of_card_leproof · cited by 1
- CategoryTheory.Functor.eventually_injectiveproof · cited by 0
- Fin.le_of_surjectiveproof · cited by 0
- NumberField.InfinitePlace.card_monoproof · cited by 0
- Fintype.card_quotient_leproof · cited by 0